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Subgroup temperaments

Edit 2 55 …
2.3.7 | 2.3.11 | 2.3.5.11 | 2.3.7.11 | 2.3.7.11.13 | 2.3.5.11 | 2.9.7.11 | 2.9.15.7.11.13 | 2.9.21 | 2.3.7/5.11/5.13/5 | 2.3.7.11/5.13 | 2.5.7 Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on Chromatic pairs.

2.3.7


Semaphore

Comma: 49/48

POL2 generator: ~8/7~7/6 = 250.385

Gencom: [2 8/7; 49/48]
Gencom mapping: [<1 2 0 3|, <0 -2 0 -1|]

Map: [<1 2 3|, <0 -2 -1|]
EDOs: 5, 14, 19, 24, 67c, 91c
RMS error: 2.523 cents

Archy

Archy can be thought of as "no-5's dominant" or "no-5's superpyth". The name comes from the fact that it tempers out 64/63, the Archytas comma.

Comma: 64/63

POL2 generator: ~3/2 = 709.321

Gencom: [2 3/2; 64/63]
Gencom mapping: [<1 1 0 4|, <0 1 0 -2|]

Map: [<1 2 2|, <0 -1 2|]
EDOs: 5, 12, 17, 22, 27, 137bc
RMS error: 1.856 cents

Slendric

Comma: 1029/1024

POL2 generator: ~8/7 = 233.688

Gencom: [2 8/7; 1029/1024]
Gencom mapping: [<1 1 0 3|, <0 3 0 -1|]

Map: [<1 1 3|, <0 3 -1|]
EDOs: 5, 21, 26, 31, 36, 77, 113, 190
RMS error: 0.3202 cents

Lee

Comma: 177147/175616

POL2 generator: ~81/56 = 633.525

Map: [<1 0 -3|, <0 3 11|]
EDOs: 17, 36, 89, 125, 161, 358, 519b
RMS error: 0.3519 cents

Skwares

Comma: 19683/19208

POL2 generator: ~9/7 = 425.365 cents

Map: [<1 3 6|, <0 -4 -9|]
EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc
RMS error: 1.149 cents

2.3.11


Neuter

Neuter can be thought of as the 2.3.11 version of either mohajira or maqamic, as well as suhajira (further down on this page) and ringo. Among other things, it is the temperament optimizing the neutral tetrad.

Comma: 243/242

POL2 generator: ~11/9 = 350.525

Gencom: [2 11/9; 243/242]
Gencom mapping: [<1 1 0 0 2|, <0 2 0 0 5|]

Map: [<1 1 2|, <0 2 5|]
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380
RMS error: 0.3021 cents

Seven note albitonic scale
Ten note chromatic scale
Seventeen note mega chromatic scale

2.3.5.11


Porkypine

Commas: 55/54, 100/99

POL2 generator: ~10/9 = 164.078

Gencom: [2 10/9; 55/54, 100/99]
Gencom mapping: [<1 2 3 0 4|, <0 -3 -5 0 -4|]

Map: [<1 2 3 4|, <0 -3 -5 -4|]
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd
RMS error: 2.287 cents

Mohaha

Commas: 81/80, 121/120

POL2 generator: ~11/9 = 348.094

Gencom: [2 11/9; 81/80 121/120]
Gencom mapping: [<1 1 0 0 2|, <0 2 8 0 5|]

Map: [<1 1 0 2|, <0 2 8 5|]
EDOs: 7, 10, 17, 24, 31, 55, 69d, 100d, 131bd
RMS error: 1.392 cents

Music

Mohaha10ping2 by Billy Stiltner

2.3.7.11


Ennea

Commas: 41503/41472, 43923/43904

POL2 generator: ~99/98 = 17.6258

Gencom: [2 99/98; 41503/41472, 43923/43904]
Gencom mapping: [<1 14/9 0 25/9 31/9|, <0 2 0 2 1|]

Sval map: [<9 0 11 24|, <0 2 2 1|]
EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd
RMS error: 0.0383 cents

Supra

Commas: 64/63, 99/98

POTE generator: ~3/2 = 707.192

Gencom: [2 3/2; 64/63 99/98]
Gencom mapping: [<1 1 0 4 7|, <0 1 0 -2 -6|]

Sval map: [<1 0 6 13|, <0 1 -2 -6|]
EDOs: 5, 12, 17, 39c, 56c
RMS error: 1.977 cents

Skwares

Commas: 99/98, 243/242

POTE generator: ~9/7 = 425.244

Gencom: [2 9/7; 99/98 243/242]
Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10]]

Sval map: [<1 3 6 7|, <0 -4 -9 -10|]
EDOs: 14, 17, 31, 48, 79, 127, 206bcd
RMS error: 1.099 cents

Hemif

Commas: 243/242, 896/891

POTE generator: ~11/9 = 351.535

Gencom: [2 11/9; 243/242 896/891]
Gencom mapping: [<1 1 0 -1 2|, <0 2 0 13 5|]

Sval map: [<1 1 -1 2|, <0 2 13 5|]
EDOs: 7, 17, 41, 58, 99d
RMS error: 0.6108 cents

Bleu

Commas: 99/98, 864/847

POTE generator: ~12/11 = 140.005

Map: [<1 1 2 3|, <0 5 7 4|]
EDOs: 9, 17, 43, 60c
RMS error: 1.829 cents

2.3.7.11.13


Suhajira

Commas: 64/63, 78/77, 144/143

Gencom: [2 11/9; 64/63 78/77 144/143]
Gencom map: [<1 1 0 4 2 4|, <0 2 0 -4 5 -1|]

POT2 generator: ~11/9 = 353.775

Map: [<1 1 4 2 4|, <0 2 -4 5 -1|]
EDOs: 7, 10, 17, 44d, 61cd, 78cd
RMS error: 1.953 cents

Hemif

Commas: 144/143, 243/242, 364/363
Related temperament: Hemififths, namo

POT2 generator: ~11/9 = 351.691

Gencom: [2 11/9; 144/143 243/242 364/363]
Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]

Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]
EDOs: 7, 10, 17, 24, 41, 58
RMS error: 0.7167 cents

Skwares

Commas: 78/77, 99/98, 243/242

POT2 generator: ~9/7 = 424.457

Map: [<1 3 6 7 9|, <0 -4 -9 -10 -15|]
EDOs: 17, 48e, 65de, 82c, 147ce
RMS error: 1.769 cents

Leapfrog

Commas: 169/168, 352/351, 364/363

POL2 generator: ~3/2 = 704.745 cents

Gencom: [2 3/2; 169/169 352/351 364/363]
Gencom mapping: [<1 1 0 -6 -3 -1|, <0 1 0 15 11 8|]

Sval map: [<1 0 -21 -14 -9|, <0 1 15 11 8|]
EDOs: 17, 46, 63
RMS error: 0.7541 cents

Bleu

Group: 2.3.7.11.13
Commas: 78/77, 99/98, 144/143
Sval name: 9&17

POL2 generator: ~13/12 = 139.990

Gencom: [2 13/12; 78/77 99/98 144/143]
Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]

Map: [<1 1 2 3 3|, <0 5 7 4 6|]
EDOs: 17, 43, 60c
RMS error: 1.752 cents

Parapyth (Rank 3)

Commas: 352/351, 364/363

POL2 tuning: <1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|

The gencom below gives Margo Schulter's favored basis
Gencom: [2 3/2 28/27; 352/351 364/363]
Gencom mapping: [<1 1 0 1 4 6|, <0 1 0 3 -1 -4|, <0 0 0 1 1 1|]

Sval map: [<1 0 0 7 12|, <0 1 0 -4 -7|, <0 0 1 1 1|]
EDOs: 17, 41, 46, 58, 87, 104
RMS error: 0.3789 cents

2.3.5.11


Larry

Commas: 243/242, 4000/3993
Related temperaments: gravity, harry

POTE generator: ~40/27 = 683.166

Gencom: [2 40/27; 243/242 4000/3993]
Gencom mapping: [<1 5 12 0 12|, <0 -6 -17 0 -15|]

Map: [<1 5 12 12|, <0 -6 -17 -15|]
EDOs: 7, 58, 65, 137, 202
RMS error: 0.3025 cents

2.9.7.11


Machine

Commas: 64/63, 99/98

POTE generator: ~8/7 = 214.384

Gencom: [2 8/7; 64/63 99/98]
Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]

Sval map: [<1 0 6 13|, <0 1 -1 -3|]
EDOs: 5, 6, 11, 17, 28
RMS error: 1.977 cents

Apparatus

Commas: 41503/41472, 322102/321489

POTE generator: ~77/72 = 115.570

Gencom: [2 77/72; 41503/41472 322102/321489]
Gencom mapping: [<1 5/2 0 3 5|, <0 -19/2 0 -2 -16|]

Sval map: [<1 5 3 5|, <0 -19 -2 -16|]
EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623
RMS error: 0.0673 cents

Mechanism

Commas: 896/891, 26411/26244

POTE generator: ~9/7 = 438.465

Gencom: [2 9/7; 896/891 26411/26244]
Gencom mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|]

Sval map: [<1 5 5 2|, <0 -5 -6 4|]
EDOs: 8, 11, 30, 41, 52
RMS error: 0.4262 cents

2.9.15.7.11.13


Stacks (aka 2magic)

Commas: 100/99, 105/104, 144/143, 196/195

POL2 generator: ~9/7 = 438.977

Gencom: [2 9/7; 100/99 105/104 144/143 196/195]
Gencom mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|]

Sval map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]
EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef
RMS error: 1.540 cents

2.9.15.7.11 stacks

Commas: 100/99, 225/224, 245/243

POL2 generator: ~9/7 = 438.607

Gencom: [2 9/7; 100/99 225/224 245/243]
Gencom mapping: [<1 5/2 5/2 5 2|, <0 -5/2 -1/2 -6 4|]

Sval map: [<1 0 2 -1 6|, <0 5 3 6 -4|]
EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce,
RMS error: 1.226 cents

2.9.15.7 stacks

Commas: 225/224, 245/243

POL2 generator: ~9/7 = 439.296

Gencom: [2 9/7; 225/224 245/243]
Gencom mapping: [<1 5/2 5/2 5|, <0 -5/2 -1/2 -6|]

Sval map: [<1 0 2 -1|, <0 5 3 6|]
EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c
RMS error: 1.074 cents

2.9.21

A-team

Commas: 1029/1024

POL2 generator: ~21/16 = 467.375

Gencom: [2 21/16; 1029/1024]
Gencom mapping: [<1 1 0 3|, <0 3/2 0 -1/2|]

Sval map: [<1 2 4|, <0 3 1|]
EDOs: 5, 13, 18, 41, 59, 77, 95
RMS error: 0.3202 cents

2.3.7/5.11/5.13/5

Historical

Subgroup: 2.3.7/5.11/5.13/5
Commas: 364/363, 441/440, 1001/1000

POL2 generator: ~21/20 = 83.016

Gencom: [2 21/20; 364/363 441/440 1001/1000]
Gencom map: [<1 2 -3/4 -3/4 1/4 5/4|, <0 -6 0 7 2 -9|]

Sval map: [<1 2 0 1 2|, <0 -6 7 2 -9|]
EDOs: 14, 29, 72, 101, 130, 159
RMS error: 0.2562 cents

2.3.7.11/5.13

Hypnosis

Subgroup: 2.3.7.11/5.13
Commas: 169/168, 540/539, 729/728
Related temperament: hypnos, tricot

Gencom: [2 13/9; 169/168, 540/539, 729/728]
Gencom map: [<1 0 -4 -3 4 0|, <0 3 13/2 11 -13/2 7|]

Sval map: [<1 0 -3 8 0|, <0 3 11 -13 7|]
EDOs: 17, 36, 118e, 125e, 161e, 197e
RMS error: 0.5379 cents

2.5.7


Didacus

Subgroup: 2.5.7
Commas: 3136/3125
Related temperaments: [[Chromatic+pairs#Roulette]]

Gencom: [2 28/25 3136/3125]
Gencom map: [<1 0 2 2|, <0 0 2 5|]

Sval map: [<1 2 2|, <0 2 5|]
EDOs: 6, 19, 25, 31, 37, 99, 130, 161, 353
RMS error: 0.2138 cents